{"id":5307,"date":"2022-12-21T07:00:00","date_gmt":"2022-12-21T06:00:00","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=5307"},"modified":"2023-01-03T11:01:41","modified_gmt":"2023-01-03T10:01:41","slug":"numeros-se-harshad","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/numeros-se-harshad\/","title":{"rendered":"N\u00fameros de Harshad"},"content":{"rendered":"<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Un <strong>n\u00famero de Harshad<\/strong> (en s\u00e1nscrito, <strong>gran alegr\u00eda<\/strong>) es un n\u00famero natural que es divisible por la suma de sus cifras. Su nombre se debe al matem\u00e1tico indio <strong>Dattatreya Ramachandra Kaprekar<\/strong> (1905-1986). La definici\u00f3n se extiende a n\u00fameros expresados en cualquier base num\u00e9rica, aunque los ejemplos corresponde al sistema decimal.<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Por ejemplo, el n\u00famero <strong>2023.<\/strong><\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5310\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2022\/12\/harshad.png\" alt=\"\" width=\"205\" height=\"49\"><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Los veinticinco primeros <strong>n\u00fameros de Harshad<\/strong> son:&nbsp;<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, &#8230;<\/span><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Un caso particular de los n\u00fameros de Harshad son los n\u00fameros que al dividirlos por la suma de sus cifras se obtiene un n\u00famero primo, conocidos como <strong>n\u00fameros de Moran<\/strong>.<\/span><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Los veinticinco primeros <strong>n\u00fameros de Moran<\/strong>:&nbsp;<\/span><\/p>\n<p style=\"text-align: center\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">18, 21, 27, 42, 45, 63, 84, 111, 114, 117, 133, 152, 153, 156, 171, 190, 195, 198, 201, 207, 209, 222, 228, 247, 261, &#8230;<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero de Harshad (en s\u00e1nscrito, gran alegr\u00eda) es un n\u00famero natural que es divisible por la suma de sus cifras. Su nombre se debe al matem\u00e1tico indio Dattatreya Ramachandra Kaprekar (1905-1986). La definici\u00f3n&#46;&#46;&#46;<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075204],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/5307"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=5307"}],"version-history":[{"count":7,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/5307\/revisions"}],"predecessor-version":[{"id":5336,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/5307\/revisions\/5336"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=5307"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=5307"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=5307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}